Question

b) Prove that the sum of two odd numbers is always even by two different methods.​

Answer 1

ɪꜰ ɴ ɪꜱ ᴀɴ ᴇᴠᴇɴ ɪɴᴛᴇɢᴇʀ, ᴛʜᴇɴ ᴛʜᴇʀᴇ ᴇxɪꜱᴛꜱ ᴀɴ ɪɴᴛᴇɢᴇʀ ᴋ ꜱᴜᴄʜ ᴛʜᴀᴛ ɴ = 2×ᴋ. ... ꜱɪɴᴄᴇ ᴡᴇ ꜱᴀɪᴅ ᴛʜᴀᴛ ᴀ ᴀɴᴅ ʙ ᴄᴏᴜʟᴅ ʙᴇ ᴀɴʏ ᴛᴡᴏ ᴏᴅᴅ ɪɴᴛᴇɢᴇʀꜱ, ɪᴛ ꜰᴏʟʟᴏᴡꜱ ᴛʜᴀᴛ ᴛʜᴇ ꜱᴜᴍ ᴏꜰ ᴀɴʏ ᴛᴡᴏ ᴏᴅᴅ ɪɴᴛᴇɢᴇʀꜱ ɪꜱ ᴀɴ ᴇᴠᴇɴ ɪɴᴛᴇɢᴇʀ. ᴛʜɪꜱ ᴄᴏᴍᴘʟᴇᴛᴇꜱ ᴛʜᴇ ᴘʀᴏᴏꜰ.

Answer 2

Answer:

odd number is always of the form 2n+1.(where n is a natural number)

Let a odd number be 2l+1 and the other be 2q+1,

so on adding them we get a number of the form 2l+2+2q,so it is an even number.